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Figure 17.2 Masses assigned by (a) the ysize measure; and (b) the E measure.
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Improving Mine Recognition
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1.0 0.8 Masses 0.6 0.4 0.2 0.0 (a) Friendly objects Full set 0 10 20 30 Depth (cm) 40 50 Masses
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1.0 0.8 0.6 0.4 0.2 0.0 (b) Friendly objects, D<0 Full set, D<0 Friendly objects, D>0 Full set, D>0 0 10 20 30 v (cm/ns) 40 50
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Figure 17.3 Masses assigned by (a) the depth; and (b) the velocity measure.
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5.2.3 d1 Mass Assignment
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If an object is buried too deeply, it is possibly a non-dangerous one. Otherwise, it could be anything. Following this logic, masses can be modeled as shown in Figure 17.3(a).
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5.3 GPR B-scan (Hyperbola) Measures
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5.3.1 D Mass Assignment
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Since its meaning is the same as that of d1 D is modeled as given in Figure 17.3(a).
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5.3.2 v Mass Assignment
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As mentioned earlier, the value of the propagation velocity depends on the medium, so, in the case of the soil, it should be around the values for this medium, and if it is the air, it should be close to c. In order to decide which model should be used, the sign of D is used as an indicator. If the value of v is expectable for a particular medium, an object that gives that estimation of v could be anything. If v differs significantly from the expected values for that medium, it can be expected that it is something friendly or simply background. This reasoning is illustrated in Figure 17.3(b).
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5.3.3 d/k Mass Assignment
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If this measure is within a range of values that can be expected for mines, such an object could be anything from the full set. For very low or high values of this parameter, it is quite certain that the object is non-dangerous. Following this idea, masses are modeled as shown in Figure 17.4(a).
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5.4 MD Measures
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5.4.1 Measures for MD Regions Selected by Local Maxima Analysis for Saturated Images With Windows
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The number of pixels of a region corresponds to its area, which is a highly unreliable parameter, taking into account the poor x-direction resolution in real scenarios, so we discard this information. Since the value of a local maximum depends at least on the metal content of an object and its depth,
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Modeling in Terms of Belief Functions
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1.0 0.8 Masses Masses 0.6 0.4 0.2 0.0 0 (a) 400 800 1200 1600 dk Friendly objects Full set
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1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 70 80 w_y (cm) Friendly objects Full set
Figure 17.4 Masses assigned by (a) the d/k measure; and (b) the wy measure. and since we cannot extract any of the two in any other way to our knowledge, Vmax is not useful here either. Therefore, the only remaining information whose usefulness should be discussed here, is the width of the region in the y-direction, wy . If we do not have information on the possible size of metal in the mines, we can only keep regions as they are. Consequently, if MD is used alone, we can treat all the regions as potential mines. For fusion with the other two sensors, we can also give the highest confidence of the MD in treating these regions as mines, plus providing the local maxima values in order to have a hint on its metallic content (by using the depth information of the GPR). On the other hand, if we have information on the expected sizes of metal in a minefield, we can include that information in the sense of assigning masses by this measure. For example, if it is expected that there are no mines for which the size of the metal is smaller than around 5 cm, nor larger than around 80 cm (which is quite loose in reality), we can model mass assignments by the wy measure, as given in Figure 17.4(b). This reasoning can be refined if we have additional knowledge or information about the metal content of the objects. An approach dealing with such information is proposed in [35].
5.4.2 Measures for MD Regions Selected by Local Maxima Analysis for Saturated Images Without Windows
The discussion regarding the usefulness of the first two measures, Np and Vmax , remains the same as in the previous case. Regarding wy information, this time we cannot make use of it at all, since an underlying assumption for using this type of local maxima region selection is that we do not have information on the expected sizes of objects, nor their arrangements in a minefield. This means that this is our final output, or, taking the cautious approach, that all the MD selected regions should be treated as potential mines. Therefore, in the case of fusion of MD with the other two sensors, each of these regions will have the maximum value of the mass of the full set, meaning that the ignorance is the highest possible.